The Delaunay-based mesh generation algorithms for 3D domains have been embedded in computational softwares, for example, the delaunayTriangulaion and delaunay functions in MATLAB. It has also been implemented in various software packages and toolboxes, including QualMesh [1]}, the CGAL library [2]}, [3]} for C++, TetGen program[4]}, iso2mesh [5]} built on CGAL and TetGen for MATLAB/Octave, and some MATLAB functions such as distmesh/distmeshnd [6]}. These implementations differ in their methodologies of handling domain boundaries, generating quality meshes, and input formats, and therefore are suitable for various applications. For example, the functions distmesh and distmeshnd take distance functions as representations of boundary geometry, while delaunayTriangulation generates Delaunay 2D/3D triangulation based on given point sets. If mathematical representations of boundary geometry or the vertex sets for Delaunay triangulations are not immediately available for complex real 3D objects, one can also use TetGen which requires triangular surface mesh on domain boundaries as input.
